Dynamics of an electron beam in the magnetic field of a betatron

Expressions for the vector potential and magnetic induction vector components have been obtained for a vertically asymmetric magnetic field of a betatron. The dynamics of the electron beam in the process of injection and acceleration in the electromagnetic field of the betatron has been investigated. It has been shown that the asymmetry of the magnetic field decreases the efficiency of the electron involvement in acceleration. The mutually related radial-vertical asymmetric oscillations of the electron beam in the asymmetric field lead to considerable losses of the beam particles on the walls and injector of the acceleration chamber. The results of these investigations may be useful in developing and tuning electron beam acceleration systems.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 42–46, December, 2004.